\section{Definitions}
\subsection{Lagrange-Hamilton}
A system is \emph{natural} when the Hamiltonian of the system is $T+V=E$ (the total energy).\\
A constraint is \emph{ideal} when the constraint force for each particle is perpendicular to the constraint manifold for that particle. \\
A constraint is \emph{holonomic} when it's independent of the velocities of the particles.


\subsection{Rigid body motion}
A rigid body is \emph{generic} if it contains three non-collinear particles.